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use pyo3::prelude::*;
use numpy::
{
IntoPyArray,
PyArrayDyn,
PyReadonlyArrayDyn
};
use crate::math::integrate_1d;
use crate::physics::single_chain::
{
ONE,
ZERO,
POINTS
};
pub fn register_module(py: Python<'_>, parent_module: &PyModule) -> PyResult<()>
{
let isometric = PyModule::new(py, "isometric")?;
super::legendre::py::register_module(py, isometric)?;
parent_module.add_submodule(isometric)?;
isometric.add_class::<WLC>()?;
Ok(())
}
/// The worm-like chain (WLC) model thermodynamics in the isometric ensemble.
#[pyclass]
#[derive(Copy, Clone)]
pub struct WLC
{
/// The mass of each hinge in the chain in units of kg/mol.
#[pyo3(get)]
pub hinge_mass: f64,
/// The length of each link in the chain in units of nm.
#[pyo3(get)]
pub link_length: f64,
/// The number of links in the chain.
#[pyo3(get)]
pub number_of_links: u8,
/// The persistance length of the chain in units of nm.
#[pyo3(get)]
pub persistance_length: f64,
nondimensional_persistance_length: f64,
normalization_nondimensional_equilibrium_distribution: f64,
/// The thermodynamic functions of the model in the isometric ensemble approximated using a Legendre transformation.
#[pyo3(get)]
pub legendre: super::legendre::py::WLC
}
#[pymethods]
impl WLC
{
#[new]
pub fn init(number_of_links: u8, link_length: f64, hinge_mass: f64, persistance_length: f64) -> Self
{
let nondimensional_persistance_length = persistance_length/(number_of_links as f64)/link_length;
let normalization_nondimensional_equilibrium_distribution = integrate_1d(&|nondimensional_end_to_end_length_per_link: &f64| super::nondimensional_equilibrium_radial_distribution(&nondimensional_persistance_length, &1.0, nondimensional_end_to_end_length_per_link), &ZERO, &ONE, &POINTS);
WLC
{
hinge_mass,
link_length,
number_of_links,
persistance_length,
nondimensional_persistance_length,
normalization_nondimensional_equilibrium_distribution,
legendre: super::legendre::py::WLC::init(number_of_links, link_length, hinge_mass, persistance_length)
}
}
/// The expected force as a function of the applied end-to-end length and temperature.
///
/// Args:
/// end_to_end_length (numpy.ndarray): The end-to-end length :math:`\xi`.
/// temperature (float): The temperature :math:`T`.
///
/// Returns:
/// numpy.ndarray: The force :math:`f`.
///
pub fn force<'py>(&self, py: Python<'py>, end_to_end_length: PyReadonlyArrayDyn<f64>, temperature: f64) -> &'py PyArrayDyn<f64>
{
end_to_end_length.as_array().mapv(|end_to_end_length: f64| super::force(&self.number_of_links, &self.link_length, &self.persistance_length, &end_to_end_length, &temperature)).into_pyarray(py)
}
/// The expected nondimensional force as a function of the applied nondimensional end-to-end length per link.
///
/// Args:
/// nondimensional_end_to_end_length_per_link (numpy.ndarray): The nondimensional end-to-end length per link :math:`\gamma\equiv \xi/N_b\ell_b`.
///
/// Returns:
/// numpy.ndarray: The nondimensional force :math:`\eta\equiv\beta f\ell_b`.
///
pub fn nondimensional_force<'py>(&self, py: Python<'py>, nondimensional_end_to_end_length_per_link: PyReadonlyArrayDyn<f64>) -> &'py PyArrayDyn<f64>
{
nondimensional_end_to_end_length_per_link.as_array().mapv(|nondimensional_end_to_end_length_per_link: f64| super::nondimensional_force(&self.number_of_links, &self.nondimensional_persistance_length, &nondimensional_end_to_end_length_per_link)).into_pyarray(py)
}
/// The Helmholtz free energy as a function of the applied end-to-end length and temperature,
///
/// .. math::
/// \psi(\xi, T) = -kT\ln Q(\xi, T).
///
/// Args:
/// end_to_end_length (numpy.ndarray): The end-to-end length :math:`\xi`.
/// temperature (float): The temperature :math:`T`.
///
/// Returns:
/// numpy.ndarray: The Helmholtz free energy :math:`\psi`.
///
pub fn helmholtz_free_energy<'py>(&self, py: Python<'py>, end_to_end_length: PyReadonlyArrayDyn<f64>, temperature: f64) -> &'py PyArrayDyn<f64>
{
end_to_end_length.as_array().mapv(|end_to_end_length: f64| super::helmholtz_free_energy(&self.number_of_links, &self.link_length, &self.hinge_mass, &self.persistance_length, &end_to_end_length, &temperature)).into_pyarray(py)
}
/// The Helmholtz free energy per link as a function of the applied end-to-end length and temperature.
///
/// Args:
/// end_to_end_length (numpy.ndarray): The end-to-end length :math:`\xi`.
/// temperature (float): The temperature :math:`T`.
///
/// Returns:
/// numpy.ndarray: The Helmholtz free energy per link :math:`\psi/N_b`.
///
pub fn helmholtz_free_energy_per_link<'py>(&self, py: Python<'py>, end_to_end_length: PyReadonlyArrayDyn<f64>, temperature: f64) -> &'py PyArrayDyn<f64>
{
end_to_end_length.as_array().mapv(|end_to_end_length: f64| super::helmholtz_free_energy_per_link(&self.number_of_links, &self.link_length, &self.hinge_mass, &self.persistance_length, &end_to_end_length, &temperature)).into_pyarray(py)
}
/// The relative Helmholtz free energy as a function of the applied end-to-end length and temperature,
///
/// .. math::
/// \Delta\psi(\xi, T) = kT\ln\left[\frac{P_\mathrm{eq}(0)}{P_\mathrm{eq}(\xi)}\right].
///
/// Args:
/// end_to_end_length (numpy.ndarray): The end-to-end length :math:`\xi`.
/// temperature (float): The temperature :math:`T`.
///
/// Returns:
/// numpy.ndarray: The relative Helmholtz free energy :math:`\Delta\psi\equiv\psi(\xi,T)-\psi(0,T)`.
///
pub fn relative_helmholtz_free_energy<'py>(&self, py: Python<'py>, end_to_end_length: PyReadonlyArrayDyn<f64>, temperature: f64) -> &'py PyArrayDyn<f64>
{
end_to_end_length.as_array().mapv(|end_to_end_length: f64| super::relative_helmholtz_free_energy(&self.number_of_links, &self.link_length, &self.persistance_length, &end_to_end_length, &temperature)).into_pyarray(py)
}
/// The relative Helmholtz free energy per link as a function of the applied end-to-end length and temperature.
///
/// Args:
/// end_to_end_length (numpy.ndarray): The end-to-end length :math:`\xi`.
/// temperature (float): The temperature :math:`T`.
///
/// Returns:
/// numpy.ndarray: The relative Helmholtz free energy per link :math:`\Delta\psi/N_b`.
///
pub fn relative_helmholtz_free_energy_per_link<'py>(&self, py: Python<'py>, end_to_end_length: PyReadonlyArrayDyn<f64>, temperature: f64) -> &'py PyArrayDyn<f64>
{
end_to_end_length.as_array().mapv(|end_to_end_length: f64| super::relative_helmholtz_free_energy_per_link(&self.number_of_links, &self.link_length, &self.persistance_length, &end_to_end_length, &temperature)).into_pyarray(py)
}
/// The nondimensional Helmholtz free energy as a function of the applied nondimensional end-to-end length per link and temperature.
///
/// Args:
/// nondimensional_end_to_end_length_per_link (numpy.ndarray): The nondimensional end-to-end length per link :math:`\gamma\equiv \xi/N_b\ell_b`.
/// temperature (float): The temperature :math:`T`.
///
/// Returns:
/// numpy.ndarray: The nondimensional Helmholtz free energy :math:`N_b\vartheta=\beta\psi`.
///
pub fn nondimensional_helmholtz_free_energy<'py>(&self, py: Python<'py>, nondimensional_end_to_end_length_per_link: PyReadonlyArrayDyn<f64>, temperature: f64) -> &'py PyArrayDyn<f64>
{
nondimensional_end_to_end_length_per_link.as_array().mapv(|nondimensional_end_to_end_length_per_link: f64| super::nondimensional_helmholtz_free_energy(&self.number_of_links, &self.link_length, &self.hinge_mass, &self.nondimensional_persistance_length, &nondimensional_end_to_end_length_per_link, &temperature)).into_pyarray(py)
}
/// The nondimensional Helmholtz free energy per link as a function of the applied nondimensional end-to-end length per link and temperature.
///
/// Args:
/// nondimensional_end_to_end_length_per_link (numpy.ndarray): The nondimensional end-to-end length per link :math:`\gamma\equiv \xi/N_b\ell_b`.
/// temperature (float): The temperature :math:`T`.
///
/// Returns:
/// numpy.ndarray: The nondimensional Helmholtz free energy per link :math:`\vartheta\equiv\beta\psi/N_b`.
///
pub fn nondimensional_helmholtz_free_energy_per_link<'py>(&self, py: Python<'py>, nondimensional_end_to_end_length_per_link: PyReadonlyArrayDyn<f64>, temperature: f64) -> &'py PyArrayDyn<f64>
{
nondimensional_end_to_end_length_per_link.as_array().mapv(|nondimensional_end_to_end_length_per_link: f64| super::nondimensional_helmholtz_free_energy_per_link(&self.number_of_links, &self.link_length, &self.hinge_mass, &self.nondimensional_persistance_length, &nondimensional_end_to_end_length_per_link, &temperature)).into_pyarray(py)
}
/// The nondimensional relative Helmholtz free energy as a function of the applied nondimensional end-to-end length per link,
///
/// .. math::
/// \beta\Delta\psi(\gamma) = \ln\left[\frac{\mathscr{P}_\mathrm{eq}(0)}{\mathscr{P}_\mathrm{eq}(\gamma)}\right].
///
/// Args:
/// nondimensional_end_to_end_length_per_link (numpy.ndarray): The nondimensional end-to-end length per link :math:`\gamma\equiv \xi/N_b\ell_b`.
///
/// Returns:
/// numpy.ndarray: The nondimensional relative Helmholtz free energy :math:`N_b\Delta\vartheta=\beta\Delta\psi`.
///
pub fn nondimensional_relative_helmholtz_free_energy<'py>(&self, py: Python<'py>, nondimensional_end_to_end_length_per_link: PyReadonlyArrayDyn<f64>) -> &'py PyArrayDyn<f64>
{
nondimensional_end_to_end_length_per_link.as_array().mapv(|nondimensional_end_to_end_length_per_link: f64| super::nondimensional_relative_helmholtz_free_energy(&self.nondimensional_persistance_length, &nondimensional_end_to_end_length_per_link)).into_pyarray(py)
}
/// The nondimensional relative Helmholtz free energy per link as a function of the applied nondimensional end-to-end length per link,
///
/// .. math::
/// \Delta\vartheta(\gamma) = \ln\left[\frac{\mathscr{P}_\mathrm{eq}(0)}{\mathscr{P}_\mathrm{eq}(\gamma)}\right]^{1/N_b}.
///
/// Args:
/// nondimensional_end_to_end_length_per_link (numpy.ndarray): The nondimensional end-to-end length per link :math:`\gamma\equiv \xi/N_b\ell_b`.
///
/// Returns:
/// numpy.ndarray: The nondimensional relative Helmholtz free energy per link :math:`\Delta\vartheta\equiv\beta\Delta\psi/N_b`.
///
pub fn nondimensional_relative_helmholtz_free_energy_per_link<'py>(&self, py: Python<'py>, nondimensional_end_to_end_length_per_link: PyReadonlyArrayDyn<f64>) -> &'py PyArrayDyn<f64>
{
nondimensional_end_to_end_length_per_link.as_array().mapv(|nondimensional_end_to_end_length_per_link: f64| super::nondimensional_relative_helmholtz_free_energy_per_link(&self.number_of_links, &self.nondimensional_persistance_length, &nondimensional_end_to_end_length_per_link)).into_pyarray(py)
}
/// The equilibrium probability density of end-to-end vectors as a function of the end-to-end length,
///
/// .. math::
/// P_\mathrm{eq}(\xi) = \frac{e^{-\beta\psi(\xi, T)}}{4\pi\int e^{-\beta\psi(\xi', T)} \,{\xi'}{}^2 d\xi'}.
///
/// Args:
/// end_to_end_length (numpy.ndarray): The end-to-end length :math:`\xi`.
///
/// Returns:
/// numpy.ndarray: The equilibrium probability density :math:`P_\mathrm{eq}`.
///
pub fn equilibrium_distribution<'py>(&self, py: Python<'py>, end_to_end_length: PyReadonlyArrayDyn<f64>) -> &'py PyArrayDyn<f64>
{
end_to_end_length.as_array().mapv(|end_to_end_length: f64| super::equilibrium_distribution(&self.number_of_links, &self.link_length, &self.persistance_length, &self.normalization_nondimensional_equilibrium_distribution, &end_to_end_length)).into_pyarray(py)
}
/// The nondimensional equilibrium probability density of nondimensional end-to-end vectors per link as a function of the nondimensional end-to-end length per link,
///
/// .. math::
/// \mathscr{P}_\mathrm{eq}(\gamma) = \frac{e^{-\Delta\vartheta(\gamma)}}{4\pi\int e^{-\Delta\vartheta(\gamma')} \,{\gamma'}{}^2 d\gamma'}.
///
/// Args:
/// nondimensional_end_to_end_length_per_link (numpy.ndarray): The nondimensional end-to-end length per link :math:`\gamma\equiv \xi/N_b\ell_b`.
///
/// Returns:
/// numpy.ndarray: The nondimensional equilibrium probability density :math:`\mathscr{P}_\mathrm{eq}\equiv (N_b\ell_b)^3 P_\mathrm{eq}`.
///
pub fn nondimensional_equilibrium_distribution<'py>(&self, py: Python<'py>, nondimensional_end_to_end_length_per_link: PyReadonlyArrayDyn<f64>) -> &'py PyArrayDyn<f64>
{
nondimensional_end_to_end_length_per_link.as_array().mapv(|nondimensional_end_to_end_length_per_link: f64| super::nondimensional_equilibrium_distribution(&self.nondimensional_persistance_length, &self.normalization_nondimensional_equilibrium_distribution, &nondimensional_end_to_end_length_per_link)).into_pyarray(py)
}
/// The equilibrium probability density of end-to-end lengths as a function of the end-to-end length, given by :footcite:t:`treloar1949physics` as
///
/// .. math::
/// g_\mathrm{eq}(\xi) = 4\pi\xi^2 P_\mathrm{eq}(\xi).
///
/// Args:
/// end_to_end_length (numpy.ndarray): The end-to-end length :math:`\xi`.
///
/// Returns:
/// numpy.ndarray: The equilibrium probability density :math:`g_\mathrm{eq}`.
///
pub fn equilibrium_radial_distribution<'py>(&self, py: Python<'py>, end_to_end_length: PyReadonlyArrayDyn<f64>) -> &'py PyArrayDyn<f64>
{
end_to_end_length.as_array().mapv(|end_to_end_length: f64| super::equilibrium_radial_distribution(&self.number_of_links, &self.link_length, &self.persistance_length, &self.normalization_nondimensional_equilibrium_distribution, &end_to_end_length)).into_pyarray(py)
}
/// The nondimensional equilibrium probability density of nondimensional end-to-end lengths per link as a function of the nondimensional end-to-end length per link,
///
/// .. math::
/// \mathscr{g}_\mathrm{eq}(\gamma) = 4\pi\gamma^2 \mathscr{P}_\mathrm{eq}(\gamma).
///
/// Args:
/// nondimensional_end_to_end_length_per_link (numpy.ndarray): The nondimensional end-to-end length per link :math:`\gamma\equiv \xi/N_b\ell_b`.
///
/// Returns:
/// numpy.ndarray: The nondimensional equilibrium probability density :math:`\mathscr{g}_\mathrm{eq}\equiv N_b\ell_b g_\mathrm{eq}`.
///
pub fn nondimensional_equilibrium_radial_distribution<'py>(&self, py: Python<'py>, nondimensional_end_to_end_length_per_link: PyReadonlyArrayDyn<f64>) -> &'py PyArrayDyn<f64>
{
nondimensional_end_to_end_length_per_link.as_array().mapv(|nondimensional_end_to_end_length_per_link: f64| super::nondimensional_equilibrium_radial_distribution(&self.nondimensional_persistance_length, &self.normalization_nondimensional_equilibrium_distribution, &nondimensional_end_to_end_length_per_link)).into_pyarray(py)
}
}